Parameter Inference of Black Hole Images using Deep Learning in Visibility Space

TL;DR

This study develops and tests a framework for inferring black hole parameters directly from visibility-space data measured by very long baseline interferometry, targeting the spin $a_{*}$ and the electron–ion temperature ratio parameter $R_{ ext{high}}$. Using GRMHD simulations for MAD and SANE families, the authors build static and sequential architectures (autoencoder, 1D CNN, Bi-LSTM, and multitask regressors) to map visibilities to $(a_{*}, R_{ ext{high}})$, and validate on synthetic data before applying to EHT 2017 observations of M87*. Results show strong spin recovery for SANE in static settings and notable improvements with sequential models, while MAD-based models are less reliable, especially in static form; applying to real data yields retrograde spins around $a_{*} oughly -0.76$ with substantial uncertainty in $R_{ ext{high}}$, highlighting the need for polarization information and higher-fidelity modeling. The work demonstrates the feasibility of direct visibility-domain inference and identifies key limitations and avenues (polarization, improved noise modeling, and attention-based temporal models) to enhance parameter recovery in future VLBI analyses.

Abstract

Using very long baseline interferometry, the Event Horizon Telescope (EHT) collaboration has resolved the shadows of two supermassive black holes. Model comparison is traditionally performed in image space, where imaging algorithms introduce uncertainties in the recovered structure. Here, we develop a deep learning framework to perform parameter inference in visibility space, directly using the data measured by the interferometer without introducing potential errors and biases from image reconstruction. First, we train and validate our framework on synthetic data derived from general relativistic magnetohydrodynamics (GRMHD) simulations that vary in magnetic field state, spin, and $R_\mathrm{high}$. Applying these models to the real data obtained during the 2017 EHT campaign, and only considering total intensity, we do not derive meaningful constraints on either of these parameters. At present, our method is limited both by theoretical uncertainties in the GRMHD simulations and variation between snapshots of the same underlying physical model. However, we demonstrate that spin and $R_\mathrm{high}$ could be recovered using this framework through continuous monitoring of our sources, which mitigates variations due to turbulence. In future work, we anticipate that including spectral or polarimetric information will greatly improve the performance of this framework.

Figures (11)

• Figure 1: Gallery of example MAD snapshots used in this study. Snapshots are plotted on a logarithmic scale with three orders of magnitude of dynamic range to better visualize low surface brightness details. Simulations with different values of $a$ are shown in different columns, and simulations with different values of $R_\mathrm{high}$ are shown in different rows.
• Figure 2: As \ref{['fig:mad_gallery']}, but for our SANE models. These models exhibit more obvious sensitivity to $a$ and $R_\mathrm{high}$, leading us to expect that parameter inference should be easier for SANEs than for MADs.
• Figure 3: The architecture of the entire pipeline for non-sequential models processes radio images of shape $B \times M \times 4$, where $B$ represents the number of radio images in a batch, $M$ denotes the number of frequency values in each radio image, and the four channels correspond to the $u$, $v$, $\Re$ (real part), and $\Im$ (imaginary part) components. The encoder transforms the original data into a vector $Z$, where $Z \in \mathbb{R}^{50}$. A 1D CNN takes $Z$ as input and outputs a 128-dimensional vector. Finally, two fully connected neural networks (FCNNs) map this to two single output variables: $\hat{a_*}$ or $\hat{R}_{\text{high}}$.
• Figure 4: The architecture of the entire pipeline for sequential models processes radio images of shape $B \times T \times M \times 4$, where $B$ represents the batch size, $T$ denotes the number of frames, $M$ corresponds to the number of frequency values in each radio image, and the four channels represent the $u$, $v$, $\Re$ (real part), and $\Im$ (imaginary part) components. The encoder transforms the original data into a sequence of vectors $Z_t$, where $Z_t \in \mathbb{R}^{50}$. The language model (LM), which is a Bi-LSTM, is trained in a self-supervised fashion using the sequence of $Z_t$ as input, learning by predicting masked $Z_j$ values. After pretraining the LM, the Bi-LSTM network trained in the LM step is fine-tuned to generate a 128-dimensional embedding, which is then fed into a fully connected neural network (FCNN) to predict $\hat{a_*}$ and $\hat{R}_{\text{high}}$.
• Figure 5: The architecture encodes radio images, starting with the encoder, where the original data is processed, and then moves to the decoder, which generates the reconstructed version. When the decoder is removed, the original data is transformed into a 50-dimensional vector $Z$.